Distribution of Random-Flight Chains in Solution near Convex Barriers

Abstract

Equilibrium distributions of random-flight linear polymer chains in solution near impenetrable convex barriers are derived for two models: a sphere and a long circular cylinder immersed in the polymer solution. As was shown earlier for chains restricted to one side of an infinite plane interface, the entropic repulsion due to the constraint on chain conformations causes a redistribution of chain segments, with interior segments being more strongly rejected than chain ends as the total segment concentration vanishes at the interface. As the polymer chain length increases, the segment distribution at the interface becomes progressively dependent on the curvature of the boundary, and significant differences in the polymer segment distributions develop among the models. For long chains about a sphere, segment concentration profiles (normalized to unit concentration in the bulk phase) are asymptotically independent of chain length, whereas no such limit is found for the plane or cylinder. The most noticeable feature of segment profiles for long chains about a cylinder is that the concentration of chain ends is nearly proportional to the logarithm of the radial distance from the cylinder axis over a surprisingly large distance range, which increases with chain length. The average thickness of the “depletion layer” at the spherical and cylindrical interfaces is calculated and correlated with chain length and curvature of the barrier. Finally, the segment distribution of star-shaped branched chains at the spherical interface is discussed briefly.